is it possible to use vector index in a while function?

Making a very slight change to your code, use the length() function check the length (number of elements) of fib before each iteration of the while loop.

while(length(fib)<100){....}

This way you avoid creating a further variable to count the number of iterations, as in the other answers.

For what it’s worth, this is how I would do it – a for loop is more appropriate as you have a set number of iterations

n <- 100
fib <- c(0,1)

for(i in 3:n){
  fib[i] <- fib[i-2] + fib[i-1]
}